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Block #2,762,376

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/24/2018, 1:17:20 AM Β· Difficulty 11.6551 Β· 4,076,027 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7936aa5bc05e70516ddd81ebc518381595abfe59df8b2b7ee9054cadeb48b075
View on Chainz β†—

Height

#2,762,376

Difficulty

11.655078

Transactions

2

Size

1017 B

Version

2

Bits

0ba7b329

Nonce

263,579,264

Timestamp

7/24/2018, 1:17:20 AM

Confirmations

4,076,027

Mined by

⛏️ P2SHASm6K4gk11d4riWMcPavdtUuXwT9ebniFL

Merkle Root

468bc3c545dfaafb56f71e8e274b40e1201050bea014c4fcb651f3f40b990616
Transactions (2)
Coinbasedba2437d2f8895…60b987ffb508bc
1 in β†’ 1 out7.3600 XPM110 B
ASm6K4gk…T9ebniFL
88708a5c955f76…0b390d204923fa
5 in β†’ 2 out4223.4704 XPM816 B
AWSSNBdL…i5WLU5ANAVNeNeap…pY8N13sR
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.

7.892 Γ— 10⁹⁡(96-digit number)
78928063234901189074…14219717020978380799
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
7.892 Γ— 10⁹⁡(96-digit number)
78928063234901189074…14219717020978380799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.892 Γ— 10⁹⁡(96-digit number)
78928063234901189074…14219717020978380801
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
1.578 Γ— 10⁹⁢(97-digit number)
15785612646980237814…28439434041956761599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.578 Γ— 10⁹⁢(97-digit number)
15785612646980237814…28439434041956761601
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
3.157 Γ— 10⁹⁢(97-digit number)
31571225293960475629…56878868083913523199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.157 Γ— 10⁹⁢(97-digit number)
31571225293960475629…56878868083913523201
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
6.314 Γ— 10⁹⁢(97-digit number)
63142450587920951259…13757736167827046399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.314 Γ— 10⁹⁢(97-digit number)
63142450587920951259…13757736167827046401
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
1.262 Γ— 10⁹⁷(98-digit number)
12628490117584190251…27515472335654092799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.262 Γ— 10⁹⁷(98-digit number)
12628490117584190251…27515472335654092801
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
2.525 Γ— 10⁹⁷(98-digit number)
25256980235168380503…55030944671308185599
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
Circulating Supply:57,951,495 XPMΒ·at block #6,838,402 Β· updates every 60s
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