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Block #2,637,020

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 7:15:21 PM Β· Difficulty 11.4153 Β· 4,201,018 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
efd6dfe2d658f1fc3745cde1be85857f31c8bf1295a3414bdcbd88bd85ae1a54
View on Chainz β†—

Height

#2,637,020

Difficulty

11.415287

Transactions

1

Size

199 B

Version

2

Bits

0b6a5041

Nonce

1,240,991,494

Timestamp

4/29/2018, 7:15:21 PM

Confirmations

4,201,018

Mined by

⛏️ P2SHAaxBjEuC9G174furRo9doBZLWrBmHNhc8C

Merkle Root

de28b4825c9d3ea12f62a9c79ac8f2383e24263bd5f1548622d5f23b49d81345
Transactions (1)
Coinbasede28b4825c9d3e…d5f23b49d81345
1 in β†’ 1 out7.6600 XPM109 B
AaxBjEuC…BmHNhc8C
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.

3.848 Γ— 10⁹⁴(95-digit number)
38489760160215840492…06144155675861179999
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
3.848 Γ— 10⁹⁴(95-digit number)
38489760160215840492…06144155675861179999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.848 Γ— 10⁹⁴(95-digit number)
38489760160215840492…06144155675861180001
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
7.697 Γ— 10⁹⁴(95-digit number)
76979520320431680984…12288311351722359999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.697 Γ— 10⁹⁴(95-digit number)
76979520320431680984…12288311351722360001
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
1.539 Γ— 10⁹⁡(96-digit number)
15395904064086336196…24576622703444719999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.539 Γ— 10⁹⁡(96-digit number)
15395904064086336196…24576622703444720001
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
3.079 Γ— 10⁹⁡(96-digit number)
30791808128172672393…49153245406889439999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.079 Γ— 10⁹⁡(96-digit number)
30791808128172672393…49153245406889440001
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
6.158 Γ— 10⁹⁡(96-digit number)
61583616256345344787…98306490813778879999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.158 Γ— 10⁹⁡(96-digit number)
61583616256345344787…98306490813778880001
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
1.231 Γ— 10⁹⁢(97-digit number)
12316723251269068957…96612981627557759999
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:57,948,655 XPMΒ·at block #6,838,037 Β· updates every 60s
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