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Block #3,153,425

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/24/2019, 12:40:07 PM Β· Difficulty 11.3226 Β· 3,684,988 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0483fddcdf040f52cd85a70057da37f70807fbcbec922e4b0f50cebb4630a757
View on Chainz β†—

Height

#3,153,425

Difficulty

11.322564

Transactions

2

Size

394 B

Version

2

Bits

0b529393

Nonce

1,152,116,405

Timestamp

4/24/2019, 12:40:07 PM

Confirmations

3,684,988

Mined by

⛏️ P2SHARbm48qRsZyALB7gqdgsMMKGGA9xQc8DBX

Merkle Root

a4edb25db82916a5324b2b332a35de800c4f7267df700aa1835d728f814db7b7
Transactions (2)
Coinbasec4211f10775cf4…85575739d4e3ea
1 in β†’ 1 out7.8000 XPM110 B
ARbm48qR…9xQc8DBX
3aa36027e6efc5…92f6f4f422fef3
1 in β†’ 1 out199.5800 XPM192 B
AeTHTL7A…vT1872bk
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.

4.022 Γ— 10⁹⁸(99-digit number)
40228009353107200478…17046514252817612799
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
4.022 Γ— 10⁹⁸(99-digit number)
40228009353107200478…17046514252817612799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.022 Γ— 10⁹⁸(99-digit number)
40228009353107200478…17046514252817612801
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
8.045 Γ— 10⁹⁸(99-digit number)
80456018706214400957…34093028505635225599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.045 Γ— 10⁹⁸(99-digit number)
80456018706214400957…34093028505635225601
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
1.609 Γ— 10⁹⁹(100-digit number)
16091203741242880191…68186057011270451199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.609 Γ— 10⁹⁹(100-digit number)
16091203741242880191…68186057011270451201
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
3.218 Γ— 10⁹⁹(100-digit number)
32182407482485760383…36372114022540902399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.218 Γ— 10⁹⁹(100-digit number)
32182407482485760383…36372114022540902401
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
6.436 Γ— 10⁹⁹(100-digit number)
64364814964971520766…72744228045081804799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.436 Γ— 10⁹⁹(100-digit number)
64364814964971520766…72744228045081804801
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
1.287 Γ— 10¹⁰⁰(101-digit number)
12872962992994304153…45488456090163609599
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:57,951,577 XPMΒ·at block #6,838,412 Β· updates every 60s
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