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Block #2,592,070

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/30/2018, 2:33:12 AM Β· Difficulty 11.3203 Β· 4,233,220 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
345b0b2a28a04bcd01f4b794406eea46c44b73aaf96715d5abadb03e086f0384
View on Chainz β†—

Height

#2,592,070

Difficulty

11.320301

Transactions

2

Size

1.14 KB

Version

2

Bits

0b51ff45

Nonce

1,068,944,481

Timestamp

3/30/2018, 2:33:12 AM

Confirmations

4,233,220

Mined by

⛏️ P2SHAWxn6iqEe8pDkQfirgGMYR3P7rJq91ywWS

Merkle Root

fe5f3544e342f490cd441b2e1d321320ea5843f72f7baefaf60d7bc8f559262e
Transactions (2)
Coinbaseabd1c66fd68599…294cc28ef05fb1
1 in β†’ 1 out7.8000 XPM110 B
AWxn6iqE…Jq91ywWS
5612c7dcd5882e…0d6259b82ba248
6 in β†’ 2 out30008.8200 XPM967 B
AY1KAUo3…Ehvh869AAUH6xbe2…UTMKYBJG
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.

5.439 Γ— 10⁹⁡(96-digit number)
54390884599238144766…53758992905018150399
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
5.439 Γ— 10⁹⁡(96-digit number)
54390884599238144766…53758992905018150399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.439 Γ— 10⁹⁡(96-digit number)
54390884599238144766…53758992905018150401
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
1.087 Γ— 10⁹⁢(97-digit number)
10878176919847628953…07517985810036300799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.087 Γ— 10⁹⁢(97-digit number)
10878176919847628953…07517985810036300801
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
2.175 Γ— 10⁹⁢(97-digit number)
21756353839695257906…15035971620072601599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.175 Γ— 10⁹⁢(97-digit number)
21756353839695257906…15035971620072601601
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
4.351 Γ— 10⁹⁢(97-digit number)
43512707679390515812…30071943240145203199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.351 Γ— 10⁹⁢(97-digit number)
43512707679390515812…30071943240145203201
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
8.702 Γ— 10⁹⁢(97-digit number)
87025415358781031625…60143886480290406399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.702 Γ— 10⁹⁢(97-digit number)
87025415358781031625…60143886480290406401
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
1.740 Γ— 10⁹⁷(98-digit number)
17405083071756206325…20287772960580812799
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:57,846,420 XPMΒ·at block #6,825,289 Β· updates every 60s
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