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Block #2,639,460

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/30/2018, 4:01:31 PM Β· Difficulty 11.5386 Β· 4,191,821 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f73186160cf2581bfe94957251e9b17061646dd92e44a2c5f43ace6f60b37aaf
View on Chainz β†—

Height

#2,639,460

Difficulty

11.538629

Transactions

1

Size

202 B

Version

2

Bits

0b89e399

Nonce

649,420,892

Timestamp

4/30/2018, 4:01:31 PM

Confirmations

4,191,821

Mined by

⛏️ P2SHAV6HS4jMPT3EkNhhjKTUoSYMACqyjZCkco

Merkle Root

d1886d04f0d53546cb59d51bcd77397d5e57a3ce6b8192ab95919250de5c096a
Transactions (1)
Coinbased1886d04f0d535…919250de5c096a
1 in β†’ 1 out7.5000 XPM110 B
AV6HS4jM…qyjZCkco
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.

5.406 Γ— 10⁹⁸(99-digit number)
54068533673030147795…33654665749221867519
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
5.406 Γ— 10⁹⁸(99-digit number)
54068533673030147795…33654665749221867519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.406 Γ— 10⁹⁸(99-digit number)
54068533673030147795…33654665749221867521
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
1.081 Γ— 10⁹⁹(100-digit number)
10813706734606029559…67309331498443735039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.081 Γ— 10⁹⁹(100-digit number)
10813706734606029559…67309331498443735041
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
2.162 Γ— 10⁹⁹(100-digit number)
21627413469212059118…34618662996887470079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.162 Γ— 10⁹⁹(100-digit number)
21627413469212059118…34618662996887470081
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
4.325 Γ— 10⁹⁹(100-digit number)
43254826938424118236…69237325993774940159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.325 Γ— 10⁹⁹(100-digit number)
43254826938424118236…69237325993774940161
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
8.650 Γ— 10⁹⁹(100-digit number)
86509653876848236472…38474651987549880319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.650 Γ— 10⁹⁹(100-digit number)
86509653876848236472…38474651987549880321
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
1.730 Γ— 10¹⁰⁰(101-digit number)
17301930775369647294…76949303975099760639
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:57,894,392 XPMΒ·at block #6,831,280 Β· updates every 60s
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