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Block #2,764,073

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/25/2018, 4:03:25 AM Β· Difficulty 11.6612 Β· 4,068,943 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9cfd0241544ddb01fac898f612cd64ea3196ab94a0512e2c5c0b6fd438099ab9
View on Chainz β†—

Height

#2,764,073

Difficulty

11.661205

Transactions

2

Size

722 B

Version

2

Bits

0ba944b5

Nonce

2,035,265,352

Timestamp

7/25/2018, 4:03:25 AM

Confirmations

4,068,943

Mined by

⛏️ P2SHAPPe8LgWdRVVoDAfs1M5LZhtZRDNgUA4Vc

Merkle Root

a3e4491f31fdcee7cdb51e45217d92e2c671580de97276aec2ffbdaa25c6b62c
Transactions (2)
Coinbase2491af6d1eb3d4…4eac4ad1088fc3
1 in β†’ 1 out7.3500 XPM109 B
APPe8LgW…DNgUA4Vc
df01b7c27ff15f…499f04858aabce
3 in β†’ 2 out480.0100 XPM523 B
AS5mxtL2…Py8WbzVaAbKsgpKm…meMyn6QD
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.

2.575 Γ— 10⁹⁴(95-digit number)
25751079353780719112…59238235967328310399
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
2.575 Γ— 10⁹⁴(95-digit number)
25751079353780719112…59238235967328310399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.575 Γ— 10⁹⁴(95-digit number)
25751079353780719112…59238235967328310401
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
5.150 Γ— 10⁹⁴(95-digit number)
51502158707561438224…18476471934656620799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.150 Γ— 10⁹⁴(95-digit number)
51502158707561438224…18476471934656620801
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
1.030 Γ— 10⁹⁡(96-digit number)
10300431741512287644…36952943869313241599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.030 Γ— 10⁹⁡(96-digit number)
10300431741512287644…36952943869313241601
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
2.060 Γ— 10⁹⁡(96-digit number)
20600863483024575289…73905887738626483199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.060 Γ— 10⁹⁡(96-digit number)
20600863483024575289…73905887738626483201
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
4.120 Γ— 10⁹⁡(96-digit number)
41201726966049150579…47811775477252966399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.120 Γ— 10⁹⁡(96-digit number)
41201726966049150579…47811775477252966401
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
8.240 Γ— 10⁹⁡(96-digit number)
82403453932098301159…95623550954505932799
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:57,908,303 XPMΒ·at block #6,833,015 Β· updates every 60s
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