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Block #2,924,982

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/16/2018, 5:10:53 AM Β· Difficulty 11.3563 Β· 3,918,005 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
31728f54fbb70320184c8bbff71ad1def15db794697f52aa9dcf8b69c31b4dcb
View on Chainz β†—

Height

#2,924,982

Difficulty

11.356324

Transactions

1

Size

201 B

Version

2

Bits

0b5b380b

Nonce

869,032,346

Timestamp

11/16/2018, 5:10:53 AM

Confirmations

3,918,005

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

ceef5bb258873748746c5c47bf559e81cf26a4c2d2256c72b296f2d96ec3b478
Transactions (1)
Coinbaseceef5bb2588737…96f2d96ec3b478
1 in β†’ 1 out7.7400 XPM110 B
AUMQRepm…tAfKmdW1
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.

1.444 Γ— 10⁹⁢(97-digit number)
14445700017958562578…66344757683419902719
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
1.444 Γ— 10⁹⁢(97-digit number)
14445700017958562578…66344757683419902719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.444 Γ— 10⁹⁢(97-digit number)
14445700017958562578…66344757683419902721
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
2.889 Γ— 10⁹⁢(97-digit number)
28891400035917125157…32689515366839805439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.889 Γ— 10⁹⁢(97-digit number)
28891400035917125157…32689515366839805441
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
5.778 Γ— 10⁹⁢(97-digit number)
57782800071834250314…65379030733679610879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.778 Γ— 10⁹⁢(97-digit number)
57782800071834250314…65379030733679610881
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
1.155 Γ— 10⁹⁷(98-digit number)
11556560014366850062…30758061467359221759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.155 Γ— 10⁹⁷(98-digit number)
11556560014366850062…30758061467359221761
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
2.311 Γ— 10⁹⁷(98-digit number)
23113120028733700125…61516122934718443519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.311 Γ— 10⁹⁷(98-digit number)
23113120028733700125…61516122934718443521
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
4.622 Γ— 10⁹⁷(98-digit number)
46226240057467400251…23032245869436887039
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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