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Block #2,681,660

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/28/2018, 1:55:33 PM Β· Difficulty 11.6917 Β· 4,161,264 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
20f53029e151f7b4f5d706bf4c12801f8ba910b0c5292a28f5e9234b28388b2b
View on Chainz β†—

Height

#2,681,660

Difficulty

11.691657

Transactions

2

Size

1017 B

Version

2

Bits

0bb11071

Nonce

1,039,229,283

Timestamp

5/28/2018, 1:55:33 PM

Confirmations

4,161,264

Mined by

⛏️ P2SHASHBFfpokKpKYKQ7PTprGvXZLU8831voge

Merkle Root

c9989e6328240fa86abe46accc45c23df1ac1d37ce7525a769afa645116e58a1
Transactions (2)
Coinbase827d04af1d2bd1…f5bcad008368ea
1 in β†’ 1 out7.3100 XPM110 B
ASHBFfpo…8831voge
27d8c22bfd4552…a0089408d718da
5 in β†’ 2 out36.9739 XPM817 B
AVPmz695…YLJvJ9b1AR9r9PJ2…ccX37pVm
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.

3.065 Γ— 10⁹⁴(95-digit number)
30651725768633126398…78482304850556938239
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
3.065 Γ— 10⁹⁴(95-digit number)
30651725768633126398…78482304850556938239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.065 Γ— 10⁹⁴(95-digit number)
30651725768633126398…78482304850556938241
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
6.130 Γ— 10⁹⁴(95-digit number)
61303451537266252797…56964609701113876479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.130 Γ— 10⁹⁴(95-digit number)
61303451537266252797…56964609701113876481
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
1.226 Γ— 10⁹⁡(96-digit number)
12260690307453250559…13929219402227752959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.226 Γ— 10⁹⁡(96-digit number)
12260690307453250559…13929219402227752961
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
2.452 Γ— 10⁹⁡(96-digit number)
24521380614906501119…27858438804455505919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.452 Γ— 10⁹⁡(96-digit number)
24521380614906501119…27858438804455505921
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
4.904 Γ— 10⁹⁡(96-digit number)
49042761229813002238…55716877608911011839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.904 Γ— 10⁹⁡(96-digit number)
49042761229813002238…55716877608911011841
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
9.808 Γ— 10⁹⁡(96-digit number)
98085522459626004476…11433755217822023679
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:57,987,740 XPMΒ·at block #6,842,923 Β· updates every 60s
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