Block #1,254,269

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/26/2015, 8:02:41 AM · Difficulty 10.7944 · 5,560,765 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40e5897fa483ba2e79e3d95a5e3af0306f8879a1c33fe9d471847c072f3ca309

View on Chainz ↗

Height

#1,254,269

Difficulty

10.794445

Transactions

Size

1.44 KB

Version

Bits

0acb60bc

Nonce

1,488,349,071

Timestamp

9/26/2015, 8:02:41 AM

Confirmations

5,560,765

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

8117f45f98c04bd06a0158681cdf8cfd8d6f31f1a58f658d0ac85dd0e8c15614

Transactions (3)

Coinbase68007e717a78be…e2feb90710f9db

1 in → 1 out8.6050 XPM116 B

AJCEY9yy…tg97E6zm

ff690c85ec1800…4b661e5bea51ee

1 in → 2 out1.0380 XPM225 B

Aaj2BWkM…UczzpHXB AbpRCqaJ…nDJNtL6e

5b0ed80157f2a7…0e851f96c00050

1 in → 26 out99.7367 XPM1.02 KB

ARAtqwPi…tQoWiZma ATxtsKxe…NAXzXXfQ AXSveR9B…WWzhrW17 ARWu72Ri…9zgvQnfw AbVtLPAH…mUSZtgnn

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.

4.486 × 10⁹⁷(98-digit number)

44860220577774381245…27194874987964006399

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

4.486 × 10⁹⁷(98-digit number)

44860220577774381245…27194874987964006399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.486 × 10⁹⁷(98-digit number)

44860220577774381245…27194874987964006401

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

8.972 × 10⁹⁷(98-digit number)

89720441155548762490…54389749975928012799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.972 × 10⁹⁷(98-digit number)

89720441155548762490…54389749975928012801

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

1.794 × 10⁹⁸(99-digit number)

17944088231109752498…08779499951856025599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.794 × 10⁹⁸(99-digit number)

17944088231109752498…08779499951856025601

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

3.588 × 10⁹⁸(99-digit number)

35888176462219504996…17558999903712051199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.588 × 10⁹⁸(99-digit number)

35888176462219504996…17558999903712051201

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

7.177 × 10⁹⁸(99-digit number)

71776352924439009992…35117999807424102399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.177 × 10⁹⁸(99-digit number)

71776352924439009992…35117999807424102401

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 #1,254,269

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