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Block #2,925,014

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/16/2018, 5:43:27 AM Β· Difficulty 11.3563 Β· 3,920,004 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
27b4419f8ce719fd02a3503ab5a3d0cd2927aa9c5df7587f8b08e2024ad724e1
View on Chainz β†—

Height

#2,925,014

Difficulty

11.356293

Transactions

1

Size

201 B

Version

2

Bits

0b5b3609

Nonce

2,059,229,983

Timestamp

11/16/2018, 5:43:27 AM

Confirmations

3,920,004

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

6e80eb8180e28bb3c44affef4f9d983f211bb9668a72faefc0e7d69d2eea158b
Transactions (1)
Coinbase6e80eb8180e28b…e7d69d2eea158b
1 in β†’ 1 out7.7400 XPM110 B
AUhjokok…k5m93PZR
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.

2.828 Γ— 10⁹⁢(97-digit number)
28281121203086262301…88718998574034337279
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
2.828 Γ— 10⁹⁢(97-digit number)
28281121203086262301…88718998574034337279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.828 Γ— 10⁹⁢(97-digit number)
28281121203086262301…88718998574034337281
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
5.656 Γ— 10⁹⁢(97-digit number)
56562242406172524602…77437997148068674559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.656 Γ— 10⁹⁢(97-digit number)
56562242406172524602…77437997148068674561
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
1.131 Γ— 10⁹⁷(98-digit number)
11312448481234504920…54875994296137349119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.131 Γ— 10⁹⁷(98-digit number)
11312448481234504920…54875994296137349121
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
2.262 Γ— 10⁹⁷(98-digit number)
22624896962469009840…09751988592274698239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.262 Γ— 10⁹⁷(98-digit number)
22624896962469009840…09751988592274698241
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
4.524 Γ— 10⁹⁷(98-digit number)
45249793924938019681…19503977184549396479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.524 Γ— 10⁹⁷(98-digit number)
45249793924938019681…19503977184549396481
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
9.049 Γ— 10⁹⁷(98-digit number)
90499587849876039363…39007954369098792959
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:58,004,567 XPMΒ·at block #6,845,017 Β· updates every 60s
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