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Block #748,395

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/1/2014, 6:54:24 AM Β· Difficulty 10.9779 Β· 6,077,157 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5d10e166c874b769c281513af238326468278c0f61f4d5257e848a76137bb191
View on Chainz β†—

Height

#748,395

Difficulty

10.977886

Transactions

2

Size

579 B

Version

2

Bits

0afa56b6

Nonce

31,644,898

Timestamp

10/1/2014, 6:54:24 AM

Confirmations

6,077,157

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b2c5ac11ad66f63d258d8d02782629e4f13110c63c4b51723f2220cd2aee66c2
Transactions (2)
Coinbasee3d86035f05109…4463a0b0dcb98a
1 in β†’ 1 out8.2900 XPM116 B
ANSXnLY2…Sd25TjkD
9fa12d871c41b2…c56c441bc76297
2 in β†’ 2 out238.7810 XPM372 B
AXW6QchQ…G9SQ6UPCAcAFW717…V1pWEX3J
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.

9.639 Γ— 10⁹⁷(98-digit number)
96398624341132364168…09163989868258979839
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
9.639 Γ— 10⁹⁷(98-digit number)
96398624341132364168…09163989868258979839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.639 Γ— 10⁹⁷(98-digit number)
96398624341132364168…09163989868258979841
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
1.927 Γ— 10⁹⁸(99-digit number)
19279724868226472833…18327979736517959679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.927 Γ— 10⁹⁸(99-digit number)
19279724868226472833…18327979736517959681
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
3.855 Γ— 10⁹⁸(99-digit number)
38559449736452945667…36655959473035919359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.855 Γ— 10⁹⁸(99-digit number)
38559449736452945667…36655959473035919361
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
7.711 Γ— 10⁹⁸(99-digit number)
77118899472905891334…73311918946071838719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.711 Γ— 10⁹⁸(99-digit number)
77118899472905891334…73311918946071838721
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
1.542 Γ— 10⁹⁹(100-digit number)
15423779894581178266…46623837892143677439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.542 Γ— 10⁹⁹(100-digit number)
15423779894581178266…46623837892143677441
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
3.084 Γ— 10⁹⁹(100-digit number)
30847559789162356533…93247675784287354879
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:57,848,517 XPMΒ·at block #6,825,551 Β· updates every 60s
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