Block #2,925,992

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/16/2018, 10:41:26 PM · Difficulty 11.3513 · 3,918,081 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d8a56257912659f48a351f7015b54641a919dba99f596959abc9ea8ad92de0fc

View on Chainz ↗

Height

#2,925,992

Difficulty

11.351299

Transactions

Size

766 B

Version

Bits

0b59eeb5

Nonce

418,928,815

Timestamp

11/16/2018, 10:41:26 PM

Confirmations

3,918,081

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

af796dfd703cf771c8c92355a339640a032f032796ff0af8dbf3251ae879ce2f

Transactions (3)

Coinbase482c8d814dbab5…2f9db88b0f02e7

1 in → 1 out7.7700 XPM110 B

AbXwmGxD…4XXYP765

91038a3ba291f7…6c14521f451d76

1 in → 2 out7.7800 XPM191 B

AZMMMBqr…x1sqV44P AeLHLxcd…r4W7rpgo

4c792c182145e3…1537ab6c2a0d91

2 in → 2 out7.1700 XPM374 B

AYDLgDYy…AEP4Pa4p AVwresjF…f6RbRqFv

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.

2.253 × 10⁹⁶(97-digit number)

22535705402540985241…43139420457156897919

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

2.253 × 10⁹⁶(97-digit number)

22535705402540985241…43139420457156897919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.253 × 10⁹⁶(97-digit number)

22535705402540985241…43139420457156897921

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

4.507 × 10⁹⁶(97-digit number)

45071410805081970483…86278840914313795839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.507 × 10⁹⁶(97-digit number)

45071410805081970483…86278840914313795841

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

9.014 × 10⁹⁶(97-digit number)

90142821610163940967…72557681828627591679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.014 × 10⁹⁶(97-digit number)

90142821610163940967…72557681828627591681

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

1.802 × 10⁹⁷(98-digit number)

18028564322032788193…45115363657255183359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.802 × 10⁹⁷(98-digit number)

18028564322032788193…45115363657255183361

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

3.605 × 10⁹⁷(98-digit number)

36057128644065576386…90230727314510366719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.605 × 10⁹⁷(98-digit number)

36057128644065576386…90230727314510366721

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

7.211 × 10⁹⁷(98-digit number)

72114257288131152773…80461454629020733439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,925,992

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