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Block #2,647,596

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/4/2018, 12:32:13 AM Β· Difficulty 11.7608 Β· 4,184,051 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
380cd69605dbc9b71786ee507b5dc6ba36679bee8d6483b7b644d7b78ad6a560
View on Chainz β†—

Height

#2,647,596

Difficulty

11.760778

Transactions

1

Size

201 B

Version

2

Bits

0bc2c25c

Nonce

795,596,128

Timestamp

5/4/2018, 12:32:13 AM

Confirmations

4,184,051

Mined by

⛏️ P2SHARbWQuf3Z3WQygzL1JKrPGA8wqz4pxL8fP

Merkle Root

bd514b5504c9431e70a424f97c5700e0e42ccb033337c21f604dbcfd1e7ac22b
Transactions (1)
Coinbasebd514b5504c943…4dbcfd1e7ac22b
1 in β†’ 1 out7.2200 XPM110 B
ARbWQuf3…z4pxL8fP
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.

3.717 Γ— 10⁹⁢(97-digit number)
37170107251315080585…64481816661845196799
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
3.717 Γ— 10⁹⁢(97-digit number)
37170107251315080585…64481816661845196799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.717 Γ— 10⁹⁢(97-digit number)
37170107251315080585…64481816661845196801
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
7.434 Γ— 10⁹⁢(97-digit number)
74340214502630161170…28963633323690393599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.434 Γ— 10⁹⁢(97-digit number)
74340214502630161170…28963633323690393601
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
1.486 Γ— 10⁹⁷(98-digit number)
14868042900526032234…57927266647380787199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.486 Γ— 10⁹⁷(98-digit number)
14868042900526032234…57927266647380787201
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
2.973 Γ— 10⁹⁷(98-digit number)
29736085801052064468…15854533294761574399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.973 Γ— 10⁹⁷(98-digit number)
29736085801052064468…15854533294761574401
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
5.947 Γ— 10⁹⁷(98-digit number)
59472171602104128936…31709066589523148799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.947 Γ— 10⁹⁷(98-digit number)
59472171602104128936…31709066589523148801
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
1.189 Γ— 10⁹⁸(99-digit number)
11894434320420825787…63418133179046297599
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:57,897,282 XPMΒ·at block #6,831,646 Β· updates every 60s
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