Block #1,246,578

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/21/2015, 3:38:35 PM · Difficulty 10.7517 · 5,570,347 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7a461e7b9c119aa378bb632d123774f06f5de38411d917000516ea2e1475fdbd

View on Chainz ↗

Height

#1,246,578

Difficulty

10.751696

Transactions

Size

2.46 KB

Version

Bits

0ac06f28

Nonce

19,714,449

Timestamp

9/21/2015, 3:38:35 PM

Confirmations

5,570,347

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

32c89a41de7c00fe24ed68f396984bb0cf9c60d8760232f46f33b275a058f3db

Transactions (4)

Coinbase64d68f008b7452…7e15f6d85970f0

1 in → 1 out8.6800 XPM116 B

AJCEY9yy…tg97E6zm

d72e4d0d3103b7…c8dd1c99e1d105

2 in → 2 out999.9900 XPM376 B

AMRycWoF…13hkF5ou ARWpNj4r…MmFxmuow

dcc239d285161b…463fa05f9f3e0f

2 in → 2 out676.1029 XPM374 B

ANLKwi9R…VqgWbRWq ATChQ3iS…mxKKSGMb

0b253b1f1b14d1…77d073589f18f1

10 in → 2 out129.6898 XPM1.52 KB

AMRycWoF…13hkF5ou AWBWBm8a…EDKUDnfu

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.

2.966 × 10⁹⁶(97-digit number)

29660268627672757100…46017120155169560959

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

2.966 × 10⁹⁶(97-digit number)

29660268627672757100…46017120155169560959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.966 × 10⁹⁶(97-digit number)

29660268627672757100…46017120155169560961

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

5.932 × 10⁹⁶(97-digit number)

59320537255345514201…92034240310339121919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.932 × 10⁹⁶(97-digit number)

59320537255345514201…92034240310339121921

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

1.186 × 10⁹⁷(98-digit number)

11864107451069102840…84068480620678243839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.186 × 10⁹⁷(98-digit number)

11864107451069102840…84068480620678243841

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

2.372 × 10⁹⁷(98-digit number)

23728214902138205680…68136961241356487679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.372 × 10⁹⁷(98-digit number)

23728214902138205680…68136961241356487681

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

4.745 × 10⁹⁷(98-digit number)

47456429804276411360…36273922482712975359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.745 × 10⁹⁷(98-digit number)

47456429804276411360…36273922482712975361

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 #1,246,578

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