Block #2,459,736

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/6/2018, 5:10:07 AM · Difficulty 10.9546 · 4,385,619 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d6487c5cf18d1c82751dfd2259bb541fb4e494b214a9b9fb77ac4b7cf702f92d

View on Chainz ↗

Height

#2,459,736

Difficulty

10.954593

Transactions

Size

1.74 KB

Version

Bits

0af46039

Nonce

166,609,538

Timestamp

1/6/2018, 5:10:07 AM

Confirmations

4,385,619

Mined by

⛏️ P2SHARXnkcRxG7n4seffghnKRXxGE5xDSV4a1x

Merkle Root

1a863da9a8109dd1de8cb120cc4be1c9346ec6fd51b787689563888b7818430f

Transactions (4)

Coinbase1ce059d22bb512…9f7faab4c6cd68

1 in → 1 out8.3500 XPM109 B

ARXnkcRx…xDSV4a1x

a66bc7eae02af3…bda7b562c0c8d2

4 in → 2 out33.2800 XPM533 B

AbUFX9LT…acjgXq6w AdyeiHLg…J5jgg4r7

8a35a387f72951…ab930ca475ac79

1 in → 2 out763.2897 XPM226 B

ALjLjYzh…ehX7Jx55 AVgPCAXG…AuUEdwuj

3eaee522b3f130…fa0adf2d2f43c3

5 in → 2 out4.1527 XPM818 B

AXSFxxbw…MYVsTk23 AJMrMUVA…XLVBXChy

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.

1.191 × 10⁹⁶(97-digit number)

11910201485825530858…37888804182405196799

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

1.191 × 10⁹⁶(97-digit number)

11910201485825530858…37888804182405196799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.191 × 10⁹⁶(97-digit number)

11910201485825530858…37888804182405196801

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

2.382 × 10⁹⁶(97-digit number)

23820402971651061716…75777608364810393599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.382 × 10⁹⁶(97-digit number)

23820402971651061716…75777608364810393601

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

4.764 × 10⁹⁶(97-digit number)

47640805943302123432…51555216729620787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.764 × 10⁹⁶(97-digit number)

47640805943302123432…51555216729620787201

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

9.528 × 10⁹⁶(97-digit number)

95281611886604246864…03110433459241574399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.528 × 10⁹⁶(97-digit number)

95281611886604246864…03110433459241574401

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

1.905 × 10⁹⁷(98-digit number)

19056322377320849372…06220866918483148799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.905 × 10⁹⁷(98-digit number)

19056322377320849372…06220866918483148801

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,459,736

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