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Block #3,713,938

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/3/2020, 2:00:40 PM Β· Difficulty 10.8801 Β· 3,128,315 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0ac51e4530cdbd1b0fa7f4a87b481fed6a1a8c6f63611903a3f5812f51ae9e29
View on Chainz β†—

Height

#3,713,938

Difficulty

10.880135

Transactions

2

Size

7.28 KB

Version

2

Bits

0ae15080

Nonce

755,571,776

Timestamp

6/3/2020, 2:00:40 PM

Confirmations

3,128,315

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

bfd7ec6eb9e286f919b434029ced4aca535e787d2d95b39ebc50787278b12db0
Transactions (2)
Coinbase55e3e6cb50bc72…16ff179b570976
1 in β†’ 1 out8.5100 XPM109 B
ASiq2qtK…VMhmk7yL
d53935dde37124…f183660311a3c0
62 in β†’ 2 out500.0787 XPM7.08 KB
Ab5fFXVt…EC9k8a2dASiq2qtK…VMhmk7yL
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.

1.442 Γ— 10⁹⁴(95-digit number)
14420898311180143288…76621728680278973539
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
1.442 Γ— 10⁹⁴(95-digit number)
14420898311180143288…76621728680278973539
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.442 Γ— 10⁹⁴(95-digit number)
14420898311180143288…76621728680278973541
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
2.884 Γ— 10⁹⁴(95-digit number)
28841796622360286576…53243457360557947079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.884 Γ— 10⁹⁴(95-digit number)
28841796622360286576…53243457360557947081
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
5.768 Γ— 10⁹⁴(95-digit number)
57683593244720573153…06486914721115894159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.768 Γ— 10⁹⁴(95-digit number)
57683593244720573153…06486914721115894161
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
1.153 Γ— 10⁹⁡(96-digit number)
11536718648944114630…12973829442231788319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.153 Γ— 10⁹⁡(96-digit number)
11536718648944114630…12973829442231788321
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
2.307 Γ— 10⁹⁡(96-digit number)
23073437297888229261…25947658884463576639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.307 Γ— 10⁹⁡(96-digit number)
23073437297888229261…25947658884463576641
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
4.614 Γ— 10⁹⁡(96-digit number)
46146874595776458522…51895317768927153279
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:57,982,421 XPMΒ·at block #6,842,252 Β· updates every 60s
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