Block #1,246,574

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/21/2015, 3:35:42 PM · Difficulty 10.7517 · 5,578,989 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

01447405f0bde83de9bbec1bc2298f62a6348e0c350f916ffc57c846d612e555

View on Chainz ↗

Height

#1,246,574

Difficulty

10.751683

Transactions

Size

1.93 KB

Version

Bits

0ac06e4a

Nonce

477,689,469

Timestamp

9/21/2015, 3:35:42 PM

Confirmations

5,578,989

Mined by

⛏️ P2SHAcqEcnG89Maw3LUkbtcbE32AHJLhtmwZM9

Merkle Root

084ef189a9a26521bf2b53630554a8c197372a09e2c95c5e70a4a30c35dba91d

Transactions (3)

Coinbase1cecbd55829d0a…74db3d3baa88d9

1 in → 1 out8.6700 XPM109 B

AcqEcnG8…LhtmwZM9

dc8972466ae43c…ddea4e6d6651d9

9 in → 2 out139.5970 XPM1.38 KB

AepJhsN7…CtxwAHPT ANLKwi9R…VqgWbRWq

c1bc73e1188ad2…91012e1b522632

2 in → 2 out10.6181 XPM373 B

AGdnTpwX…N1gXejnZ AZpeGnSF…4cbyDNBL

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.

3.317 × 10⁹²(93-digit number)

33177105077216484259…76755029382632802959

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

3.317 × 10⁹²(93-digit number)

33177105077216484259…76755029382632802959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.317 × 10⁹²(93-digit number)

33177105077216484259…76755029382632802961

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

6.635 × 10⁹²(93-digit number)

66354210154432968519…53510058765265605919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.635 × 10⁹²(93-digit number)

66354210154432968519…53510058765265605921

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

1.327 × 10⁹³(94-digit number)

13270842030886593703…07020117530531211839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.327 × 10⁹³(94-digit number)

13270842030886593703…07020117530531211841

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

2.654 × 10⁹³(94-digit number)

26541684061773187407…14040235061062423679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.654 × 10⁹³(94-digit number)

26541684061773187407…14040235061062423681

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

5.308 × 10⁹³(94-digit number)

53083368123546374815…28080470122124847359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.308 × 10⁹³(94-digit number)

53083368123546374815…28080470122124847361

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 #1,246,574

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