Block #554,756

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/21/2014, 2:47:21 AM · Difficulty 10.9626 · 6,262,165 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

029c7d37f12f43583fe1ee3061cb3a959d3368532d05a8c7b007df299b4c8f6e

View on Chainz ↗

Height

#554,756

Difficulty

10.962585

Transactions

Size

950 B

Version

Bits

0af66c00

Nonce

386,858,238

Timestamp

5/21/2014, 2:47:21 AM

Confirmations

6,262,165

Mined by

⛏️ P2SHAKFiakLxZgJ4thNkQUTfDLPSQWruePNFB7

Merkle Root

2858e4c6f5c600f9661cb0e7418a96f81bd96856e2a93430de9e46f053420ad8

Transactions (3)

Coinbasedcac7c0da4da4d…836bc53886ff4a

1 in → 1 out8.3300 XPM109 B

AKFiakLx…ruePNFB7

32175c4183d203…18b325a2ec5703

3 in → 2 out47.0170 XPM522 B

AaQLbNwC…ewutsUWb AJxs4no1…8UYbpoQY

f348990928c519…78ca455b87419b

1 in → 2 out3.1510 XPM227 B

AaZsJzzX…LeCTxcW1 AdbPWC3p…S5dNe9rK

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.

7.707 × 10⁹⁹(100-digit number)

77071086383005327229…96425602335872122879

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

7.707 × 10⁹⁹(100-digit number)

77071086383005327229…96425602335872122879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.707 × 10⁹⁹(100-digit number)

77071086383005327229…96425602335872122881

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

1.541 × 10¹⁰⁰(101-digit number)

15414217276601065445…92851204671744245759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.541 × 10¹⁰⁰(101-digit number)

15414217276601065445…92851204671744245761

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

3.082 × 10¹⁰⁰(101-digit number)

30828434553202130891…85702409343488491519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.082 × 10¹⁰⁰(101-digit number)

30828434553202130891…85702409343488491521

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

6.165 × 10¹⁰⁰(101-digit number)

61656869106404261783…71404818686976983039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.165 × 10¹⁰⁰(101-digit number)

61656869106404261783…71404818686976983041

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

1.233 × 10¹⁰¹(102-digit number)

12331373821280852356…42809637373953966079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.233 × 10¹⁰¹(102-digit number)

12331373821280852356…42809637373953966081

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 #554,756

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