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Block #2,647,364

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2018, 9:30:35 PM Β· Difficulty 11.7583 Β· 4,189,353 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
68ea23d3268444e235be25399495d86bf9a53fbba5f8b5ab9eb15145b5c0acd1
View on Chainz β†—

Height

#2,647,364

Difficulty

11.758344

Transactions

1

Size

202 B

Version

2

Bits

0bc222d8

Nonce

382,499,394

Timestamp

5/3/2018, 9:30:35 PM

Confirmations

4,189,353

Mined by

⛏️ P2SHAbWpA3cQwkvU6Lhh2mjY5UhSQ962rp3MLe

Merkle Root

56d25010f0b343b4f30f37df2d4d389fd766bde53ad8650dd6f1561705237237
Transactions (1)
Coinbase56d25010f0b343…f1561705237237
1 in β†’ 1 out7.2200 XPM110 B
AbWpA3cQ…62rp3MLe
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.

4.622 Γ— 10⁹⁸(99-digit number)
46221026447572450668…30268674693846138879
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
4.622 Γ— 10⁹⁸(99-digit number)
46221026447572450668…30268674693846138879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.622 Γ— 10⁹⁸(99-digit number)
46221026447572450668…30268674693846138881
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
9.244 Γ— 10⁹⁸(99-digit number)
92442052895144901336…60537349387692277759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.244 Γ— 10⁹⁸(99-digit number)
92442052895144901336…60537349387692277761
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
1.848 Γ— 10⁹⁹(100-digit number)
18488410579028980267…21074698775384555519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.848 Γ— 10⁹⁹(100-digit number)
18488410579028980267…21074698775384555521
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
3.697 Γ— 10⁹⁹(100-digit number)
36976821158057960534…42149397550769111039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.697 Γ— 10⁹⁹(100-digit number)
36976821158057960534…42149397550769111041
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
7.395 Γ— 10⁹⁹(100-digit number)
73953642316115921068…84298795101538222079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.395 Γ— 10⁹⁹(100-digit number)
73953642316115921068…84298795101538222081
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
1.479 Γ— 10¹⁰⁰(101-digit number)
14790728463223184213…68597590203076444159
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:57,938,018 XPMΒ·at block #6,836,716 Β· updates every 60s
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