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Block #2,468,511

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/11/2018, 8:58:56 PM Β· Difficulty 10.9601 Β· 4,376,479 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0722d7c300d70667eb95364317b242d73a149c2b8b2bbe9ff120713726239d0f
View on Chainz β†—

Height

#2,468,511

Difficulty

10.960147

Transactions

1

Size

200 B

Version

2

Bits

0af5cc33

Nonce

11,066,858

Timestamp

1/11/2018, 8:58:56 PM

Confirmations

4,376,479

Mined by

⛏️ P2SHASZ5nKkbGM6ibDypPSW4V3ABJwMQfgMDES

Merkle Root

d55e65b27bbbb3836186468aef9ecb265e571e2a9f48229df96a655c564cb4e7
Transactions (1)
Coinbased55e65b27bbbb3…6a655c564cb4e7
1 in β†’ 1 out8.3100 XPM110 B
ASZ5nKkb…MQfgMDES
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

6.492 Γ— 10⁹⁡(96-digit number)
64928284249578402165…76760783340228300799
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
6.492 Γ— 10⁹⁡(96-digit number)
64928284249578402165…76760783340228300799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.492 Γ— 10⁹⁡(96-digit number)
64928284249578402165…76760783340228300801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.298 Γ— 10⁹⁢(97-digit number)
12985656849915680433…53521566680456601599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.298 Γ— 10⁹⁢(97-digit number)
12985656849915680433…53521566680456601601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.597 Γ— 10⁹⁢(97-digit number)
25971313699831360866…07043133360913203199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.597 Γ— 10⁹⁢(97-digit number)
25971313699831360866…07043133360913203201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
5.194 Γ— 10⁹⁢(97-digit number)
51942627399662721732…14086266721826406399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.194 Γ— 10⁹⁢(97-digit number)
51942627399662721732…14086266721826406401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.038 Γ— 10⁹⁷(98-digit number)
10388525479932544346…28172533443652812799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.038 Γ— 10⁹⁷(98-digit number)
10388525479932544346…28172533443652812801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.077 Γ— 10⁹⁷(98-digit number)
20777050959865088693…56345066887305625599
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
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