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Block #2,865,596

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/3/2018, 3:07:56 PM Β· Difficulty 11.6688 Β· 3,976,130 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
93d2524b4f480c1879fc1615bb20aac3f8d34f3ae23d2cebe05b0bf6e4156372
View on Chainz β†—

Height

#2,865,596

Difficulty

11.668827

Transactions

1

Size

200 B

Version

2

Bits

0bab383c

Nonce

962,748,484

Timestamp

10/3/2018, 3:07:56 PM

Confirmations

3,976,130

Mined by

⛏️ P2SHAZrA1oH3XEek9xwsxeyxmY1LiDUSZQ8ieQ

Merkle Root

565c31a11310613c37149e74fcd0927e5a45783688467a3d4312da0b44c40b61
Transactions (1)
Coinbase565c31a1131061…12da0b44c40b61
1 in β†’ 1 out7.3300 XPM110 B
AZrA1oH3…USZQ8ieQ
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.

2.408 Γ— 10⁹⁡(96-digit number)
24088029231286182034…09169007164905471999
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
2.408 Γ— 10⁹⁡(96-digit number)
24088029231286182034…09169007164905471999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.408 Γ— 10⁹⁡(96-digit number)
24088029231286182034…09169007164905472001
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
4.817 Γ— 10⁹⁡(96-digit number)
48176058462572364069…18338014329810943999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.817 Γ— 10⁹⁡(96-digit number)
48176058462572364069…18338014329810944001
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
9.635 Γ— 10⁹⁡(96-digit number)
96352116925144728138…36676028659621887999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.635 Γ— 10⁹⁡(96-digit number)
96352116925144728138…36676028659621888001
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
1.927 Γ— 10⁹⁢(97-digit number)
19270423385028945627…73352057319243775999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.927 Γ— 10⁹⁢(97-digit number)
19270423385028945627…73352057319243776001
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
3.854 Γ— 10⁹⁢(97-digit number)
38540846770057891255…46704114638487551999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.854 Γ— 10⁹⁢(97-digit number)
38540846770057891255…46704114638487552001
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
7.708 Γ— 10⁹⁢(97-digit number)
77081693540115782510…93408229276975103999
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:57,978,188 XPMΒ·at block #6,841,725 Β· updates every 60s
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