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Block #2,701,323

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/11/2018, 8:58:40 PM Β· Difficulty 11.6307 Β· 4,135,592 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a2cba10120061ac090c4e51e6be3897c4513fc7999bf6900bf31a8971c6237a6
View on Chainz β†—

Height

#2,701,323

Difficulty

11.630679

Transactions

2

Size

574 B

Version

2

Bits

0ba17426

Nonce

688,193,237

Timestamp

6/11/2018, 8:58:40 PM

Confirmations

4,135,592

Mined by

⛏️ P2SHARvS3jyKfSQyezCyQybVzD3HVjWxusdNK3

Merkle Root

ca4dbaef19df42381d4b93140545948a3c7910b89ff143f323eb85ab9afde4bf
Transactions (2)
Coinbase80c7b549104091…74d377e18cac36
1 in β†’ 1 out7.3900 XPM110 B
ARvS3jyK…WxusdNK3
8d55011cfd2c63…67efa45de85da9
2 in β†’ 2 out504.3617 XPM374 B
AdepddBi…eU9B97ytAf2mQHYa…Mj5zhbbm
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.

3.224 Γ— 10⁹⁴(95-digit number)
32244384869561294396…20115203948464812999
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
3.224 Γ— 10⁹⁴(95-digit number)
32244384869561294396…20115203948464812999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.224 Γ— 10⁹⁴(95-digit number)
32244384869561294396…20115203948464813001
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
6.448 Γ— 10⁹⁴(95-digit number)
64488769739122588793…40230407896929625999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.448 Γ— 10⁹⁴(95-digit number)
64488769739122588793…40230407896929626001
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
1.289 Γ— 10⁹⁡(96-digit number)
12897753947824517758…80460815793859251999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.289 Γ— 10⁹⁡(96-digit number)
12897753947824517758…80460815793859252001
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
2.579 Γ— 10⁹⁡(96-digit number)
25795507895649035517…60921631587718503999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.579 Γ— 10⁹⁡(96-digit number)
25795507895649035517…60921631587718504001
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
5.159 Γ— 10⁹⁡(96-digit number)
51591015791298071034…21843263175437007999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.159 Γ— 10⁹⁡(96-digit number)
51591015791298071034…21843263175437008001
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
1.031 Γ— 10⁹⁢(97-digit number)
10318203158259614206…43686526350874015999
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:57,939,614 XPMΒ·at block #6,836,914 Β· updates every 60s
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