Block #1,239,589

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/16/2015, 5:01:32 PM · Difficulty 10.7577 · 5,571,362 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3d9f11877b119ff1e68f1b4fc93146f3690a975fa99d50c7a5ca9a7195138e09

View on Chainz ↗

Height

#1,239,589

Difficulty

10.757730

Transactions

Size

886 B

Version

Bits

0ac1fa9c

Nonce

919,786,713

Timestamp

9/16/2015, 5:01:32 PM

Confirmations

5,571,362

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

e52f4c5f9720013d1960cb9a880b90a4efe2dde3d932e1dc1509e3282227bab7

Transactions (4)

Coinbasec7a7888a00cf63…56b03cd690f97c

1 in → 1 out8.6600 XPM116 B

AJCEY9yy…tg97E6zm

818b178f65cdd2…9c49c4a74186b9

1 in → 2 out8.6200 XPM227 B

APFgRTHS…6acDUtuW AJXD79Mh…8Qg7XE3E

298c52a086848f…a7a4182120e372

1 in → 2 out7.5485 XPM226 B

AeQoX4pL…puDxgq92 AcuM7XiJ…5uND8Jce

17968c10e67840…b7e813551f24cd

1 in → 2 out1.5822 XPM226 B

Ac81mjH1…YTBaDsjk AP2GxFDi…MZQBdSYt

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.

9.563 × 10⁹⁵(96-digit number)

95631767758386545462…06844897188835084319

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

9.563 × 10⁹⁵(96-digit number)

95631767758386545462…06844897188835084319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.563 × 10⁹⁵(96-digit number)

95631767758386545462…06844897188835084321

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

1.912 × 10⁹⁶(97-digit number)

19126353551677309092…13689794377670168639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.912 × 10⁹⁶(97-digit number)

19126353551677309092…13689794377670168641

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

3.825 × 10⁹⁶(97-digit number)

38252707103354618184…27379588755340337279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.825 × 10⁹⁶(97-digit number)

38252707103354618184…27379588755340337281

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

7.650 × 10⁹⁶(97-digit number)

76505414206709236369…54759177510680674559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.650 × 10⁹⁶(97-digit number)

76505414206709236369…54759177510680674561

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

1.530 × 10⁹⁷(98-digit number)

15301082841341847273…09518355021361349119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.530 × 10⁹⁷(98-digit number)

15301082841341847273…09518355021361349121

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 #1,239,589

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