Block #2,634,150

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 6:58:42 PM · Difficulty 11.2260 · 4,209,927 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f0f3ccd5827133dca58fca1402994b9f5f1c6a65683a10c5c2eeeae8229490ad

View on Chainz ↗

Height

#2,634,150

Difficulty

11.226012

Transactions

Size

1.40 KB

Version

Bits

0b39dbe6

Nonce

10,954,514

Timestamp

4/28/2018, 6:58:42 PM

Confirmations

4,209,927

Mined by

⛏️ P2SHAX4KP2XnDXgNvn2CN4uWYJgNN6YLJamDbJ

Merkle Root

0f1847c91f6e1f57a5c1a275cf131a7958f7f36f227e5d08b321ef4f38b484e3

Transactions (4)

Coinbase1dce1afd0e8879…2764767ef22b0f

1 in → 1 out7.9500 XPM110 B

AX4KP2Xn…YLJamDbJ

31376d4a8a9cbd…894c41ccb4f5b6

2 in → 2 out289.8820 XPM374 B

ARvGH25y…71QpnyQw Aa1RUBtU…DwjoGhCR

650844ae9ea371…307ede61f4eb2c

3 in → 2 out6.0138 XPM522 B

AQ2c1rDw…htJriN75 AeufDYLZ…JhnuQkNK

114e6b06ad9761…154033093e0f2f

2 in → 1 out12.3424 XPM340 B

APE1MwnQ…JUvpLg9M

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.

2.889 × 10⁹⁶(97-digit number)

28891341764949739929…98893506092302335999

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

2.889 × 10⁹⁶(97-digit number)

28891341764949739929…98893506092302335999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.889 × 10⁹⁶(97-digit number)

28891341764949739929…98893506092302336001

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

5.778 × 10⁹⁶(97-digit number)

57782683529899479859…97787012184604671999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.778 × 10⁹⁶(97-digit number)

57782683529899479859…97787012184604672001

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

1.155 × 10⁹⁷(98-digit number)

11556536705979895971…95574024369209343999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.155 × 10⁹⁷(98-digit number)

11556536705979895971…95574024369209344001

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

2.311 × 10⁹⁷(98-digit number)

23113073411959791943…91148048738418687999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.311 × 10⁹⁷(98-digit number)

23113073411959791943…91148048738418688001

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

4.622 × 10⁹⁷(98-digit number)

46226146823919583887…82296097476837375999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.622 × 10⁹⁷(98-digit number)

46226146823919583887…82296097476837376001

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

9.245 × 10⁹⁷(98-digit number)

92452293647839167774…64592194953674751999

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 #2,634,150

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