Block #2,635,749

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 4/29/2018, 8:33:29 AM · Difficulty 11.3375 · 4,196,989 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

6e0be24ba8031206066aa564c3d9d95dfd7c73e7ecaf58b5b6f800c6a7bd9e54

View on Chainz ↗

Height

#2,635,749

Difficulty

11.337464

Transactions

Size

1.52 KB

Version

Bits

0b566403

Nonce

28,717,843

Timestamp

4/29/2018, 8:33:29 AM

Confirmations

4,196,989

Mined by

⛏️ P2SHAPHngMsJrQMMsJR92Yr6WArxME1fX3GXjS

Merkle Root

f09f297fe02312f3999fd89dd6cce4eab5eb495a6456c92d3e5b5336e0a6efc2

Transactions (5)

Coinbase1e5526dcced86b…c58edc96bc51f5

1 in → 1 out7.8100 XPM110 B

APHngMsJ…1fX3GXjS

6d151b7070579f…0e57e928fa988a

2 in → 2 out200.0101 XPM374 B

Acy3ySeA…RS5XX63j AHzkHzeK…3wME2gBF

761079dfd7c4b7…e96fa987c1984f

2 in → 2 out16.0000 XPM307 B

AZCGufqJ…azYPZ2vG AJN1ao9K…CUKW4qu3

446216a7316583…d3a230719c900d

2 in → 2 out12.9600 XPM340 B

AQniKr6B…WBxoNHMB AKD48u6Z…m3tCBrYT

1f9ef2b68d6834…1aba74bb5441a8

2 in → 2 out10.9600 XPM338 B

ATZaFf1j…q7EUNDXW AGEJ7vz1…v4XYrGCh

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.052 × 10⁹²(93-digit number)

20526142625051430861…31397436619303883019

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.052 × 10⁹²(93-digit number)

20526142625051430861…31397436619303883019

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.052 × 10⁹²(93-digit number)

20526142625051430861…31397436619303883021

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

4.105 × 10⁹²(93-digit number)

41052285250102861723…62794873238607766039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.105 × 10⁹²(93-digit number)

41052285250102861723…62794873238607766041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

8.210 × 10⁹²(93-digit number)

82104570500205723447…25589746477215532079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.210 × 10⁹²(93-digit number)

82104570500205723447…25589746477215532081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.642 × 10⁹³(94-digit number)

16420914100041144689…51179492954431064159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.642 × 10⁹³(94-digit number)

16420914100041144689…51179492954431064161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.284 × 10⁹³(94-digit number)

32841828200082289378…02358985908862128319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.284 × 10⁹³(94-digit number)

32841828200082289378…02358985908862128321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

6.568 × 10⁹³(94-digit number)

65683656400164578757…04717971817724256639

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

6.568 × 10⁹³(94-digit number)

65683656400164578757…04717971817724256641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★★☆

Rarity

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #2,635,749

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