Block #1,239,823

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/16/2015, 8:55:47 PM · Difficulty 10.7577 · 5,585,499 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2d52c23b77310c61135e9330fb3e372f91ea92cccf55a4e2af43f394e7edc0e9

View on Chainz ↗

Height

#1,239,823

Difficulty

10.757681

Transactions

Size

495 B

Version

Bits

0ac1f75f

Nonce

73,508,200

Timestamp

9/16/2015, 8:55:47 PM

Confirmations

5,585,499

Mined by

⛏️ P2SHATHVRdUsn4hmDM1aQmNBrjqfP2BHaFRSsU

Merkle Root

a5c972be9e8d2796ba769830cff76ab0933bb18bd79b002e89d0d5049238317a

Transactions (2)

Coinbasee42cfdb7a2e28d…eb4b34a8c4a691

1 in → 1 out8.6400 XPM110 B

ATHVRdUs…BHaFRSsU

69f11fae8e1097…86f2620e222076

1 in → 5 out8.6200 XPM294 B

ALqEZWdP…6VPV6ooe AWVdqMHf…3TnrQBYd AcQSa8z8…7a65Dx9G AVvA9Gzu…7fxjvGRS ATrgZbVD…smHMiiTk

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.

1.323 × 10⁹⁷(98-digit number)

13235585130898514936…78711862297575219199

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

1.323 × 10⁹⁷(98-digit number)

13235585130898514936…78711862297575219199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.323 × 10⁹⁷(98-digit number)

13235585130898514936…78711862297575219201

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

2.647 × 10⁹⁷(98-digit number)

26471170261797029872…57423724595150438399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.647 × 10⁹⁷(98-digit number)

26471170261797029872…57423724595150438401

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

5.294 × 10⁹⁷(98-digit number)

52942340523594059744…14847449190300876799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.294 × 10⁹⁷(98-digit number)

52942340523594059744…14847449190300876801

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

1.058 × 10⁹⁸(99-digit number)

10588468104718811948…29694898380601753599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.058 × 10⁹⁸(99-digit number)

10588468104718811948…29694898380601753601

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

2.117 × 10⁹⁸(99-digit number)

21176936209437623897…59389796761203507199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.117 × 10⁹⁸(99-digit number)

21176936209437623897…59389796761203507201

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 #1,239,823

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