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Block #2,757,622

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2018, 3:11:09 PM Β· Difficulty 11.6665 Β· 4,045,552 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f803ed09374ac973a43e91fba776b4c76a5f44cd296b5e68df7ee2cad62c2ed5
View on Chainz β†—

Height

#2,757,622

Difficulty

11.666487

Transactions

2

Size

871 B

Version

2

Bits

0baa9ee8

Nonce

1,461,103,056

Timestamp

7/20/2018, 3:11:09 PM

Confirmations

4,045,552

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

caebcdbefe0a605be088149d0afa7e325da8749ed641ebb94ed6b7adad4de84a
Transactions (2)
Coinbasecc0287ce986e5b…0aff888a848799
1 in β†’ 1 out7.3400 XPM110 B
AZtxQr2F…7grUWrUz
3f48726a4a6d90…3ab4e4c82edf13
4 in β†’ 2 out3075.5101 XPM671 B
AZVns1NF…9D7d6RQdAVa5dYbR…j5uZYCvt
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.

5.036 Γ— 10⁹³(94-digit number)
50368772885100829144…60572712229949330319
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
5.036 Γ— 10⁹³(94-digit number)
50368772885100829144…60572712229949330319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.036 Γ— 10⁹³(94-digit number)
50368772885100829144…60572712229949330321
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
1.007 Γ— 10⁹⁴(95-digit number)
10073754577020165828…21145424459898660639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.007 Γ— 10⁹⁴(95-digit number)
10073754577020165828…21145424459898660641
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
2.014 Γ— 10⁹⁴(95-digit number)
20147509154040331657…42290848919797321279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.014 Γ— 10⁹⁴(95-digit number)
20147509154040331657…42290848919797321281
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
4.029 Γ— 10⁹⁴(95-digit number)
40295018308080663315…84581697839594642559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.029 Γ— 10⁹⁴(95-digit number)
40295018308080663315…84581697839594642561
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
8.059 Γ— 10⁹⁴(95-digit number)
80590036616161326631…69163395679189285119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.059 Γ— 10⁹⁴(95-digit number)
80590036616161326631…69163395679189285121
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
1.611 Γ— 10⁹⁡(96-digit number)
16118007323232265326…38326791358378570239
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:57,669,409 XPMΒ·at block #6,803,173 Β· updates every 60s
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