Block #1,416,254

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/16/2016, 9:58:36 PM · Difficulty 10.7960 · 5,393,507 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

30754248415c4781763aaa60027b22f9b27737e2c07519c61ff80179ef7513d5

View on Chainz ↗

Height

#1,416,254

Difficulty

10.795955

Transactions

Size

3.90 KB

Version

Bits

0acbc3bc

Nonce

717,273,480

Timestamp

1/16/2016, 9:58:36 PM

Confirmations

5,393,507

Mined by

⛏️ P2SHAG1aYuC7zzKx98RGswpFHgjNe4uujMeARi

Merkle Root

9b9be24e229997e842b6b0763f2f377664a77532d43c0e47885e87f56070b15e

Transactions (3)

Coinbase6cdc8352fedd24…22d8f2fc43f534

1 in → 1 out8.6100 XPM109 B

AG1aYuC7…uujMeARi

62875eaed6ee4b…ee6bbee705fae3

1 in → 51 out48.0187 XPM1.85 KB

AUPQa75X…duCxbEpn AS4rujS9…Jk8M4BdJ AZ2Dv6vs…YoKVyFme APcD6Sf3…ZHxWDoS4 AJ1aDz6J…B9axufWF

70633ef9f944a6…3e6993dffec31b

5 in → 34 out0.5417 XPM1.86 KB

AStGrVds…zdrJvQyf AH2Bmenw…rPKsZyLJ AVGud9ju…t47M6tvL APsMZHS5…qBKjffrc AMBXMrmd…Xup7ZUSa

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.

5.637 × 10⁹⁴(95-digit number)

56375632484481479855…21720205238646142079

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

5.637 × 10⁹⁴(95-digit number)

56375632484481479855…21720205238646142079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.637 × 10⁹⁴(95-digit number)

56375632484481479855…21720205238646142081

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

1.127 × 10⁹⁵(96-digit number)

11275126496896295971…43440410477292284159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.127 × 10⁹⁵(96-digit number)

11275126496896295971…43440410477292284161

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

2.255 × 10⁹⁵(96-digit number)

22550252993792591942…86880820954584568319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.255 × 10⁹⁵(96-digit number)

22550252993792591942…86880820954584568321

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

4.510 × 10⁹⁵(96-digit number)

45100505987585183884…73761641909169136639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.510 × 10⁹⁵(96-digit number)

45100505987585183884…73761641909169136641

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

9.020 × 10⁹⁵(96-digit number)

90201011975170367768…47523283818338273279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.020 × 10⁹⁵(96-digit number)

90201011975170367768…47523283818338273281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.804 × 10⁹⁶(97-digit number)

18040202395034073553…95046567636676546559

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #1,416,254

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