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Block #2,911,975

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/6/2018, 3:44:36 AM Β· Difficulty 11.5200 Β· 3,921,505 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7c8d0b262d8b3a5c6ccf54543271b473661eed1f961e208702319cf6cdd6b455
View on Chainz β†—

Height

#2,911,975

Difficulty

11.519982

Transactions

2

Size

538 B

Version

2

Bits

0b851d8f

Nonce

1,066,005,613

Timestamp

11/6/2018, 3:44:36 AM

Confirmations

3,921,505

Mined by

⛏️ P2SHANWZWCi6qR54hNpnfNL3ZgzquL3macoKhG

Merkle Root

30febc3d6d857545c615c32938ccba3f038fec9a45086497398316ca4fb80b42
Transactions (2)
Coinbase11fe2273355073…50f086d94113c6
1 in β†’ 1 out7.5300 XPM110 B
ANWZWCi6…3macoKhG
c242c8a0aa8dd7…cb37828d500add
2 in β†’ 1 out123.4941 XPM338 B
AbFieDh2…UG9e4SDN
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.

2.675 Γ— 10⁹⁡(96-digit number)
26757523729872336795…60906932442563515039
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
2.675 Γ— 10⁹⁡(96-digit number)
26757523729872336795…60906932442563515039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.675 Γ— 10⁹⁡(96-digit number)
26757523729872336795…60906932442563515041
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
5.351 Γ— 10⁹⁡(96-digit number)
53515047459744673591…21813864885127030079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.351 Γ— 10⁹⁡(96-digit number)
53515047459744673591…21813864885127030081
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
1.070 Γ— 10⁹⁢(97-digit number)
10703009491948934718…43627729770254060159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.070 Γ— 10⁹⁢(97-digit number)
10703009491948934718…43627729770254060161
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
2.140 Γ— 10⁹⁢(97-digit number)
21406018983897869436…87255459540508120319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.140 Γ— 10⁹⁢(97-digit number)
21406018983897869436…87255459540508120321
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
4.281 Γ— 10⁹⁢(97-digit number)
42812037967795738873…74510919081016240639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.281 Γ— 10⁹⁢(97-digit number)
42812037967795738873…74510919081016240641
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
8.562 Γ— 10⁹⁢(97-digit number)
85624075935591477746…49021838162032481279
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:57,912,044 XPMΒ·at block #6,833,479 Β· updates every 60s
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